Automatic frequency control circuit



Sept. 9, 1952 D. LEED AUTOMATIC FREQUENCY CONTROL CRCUIT 5 Sheets-Sheet l Filed D60. 14, 1948 NF I To PHAsEb/sc.

/ REACTANCE TUBE /9 V. R M 0D A MM D m WL A m T W0 ...0, .V mw Q .w

OSC/LLATOR TUBE Jl T0 BUFFER AME /l /N F /G./

muse shi/F1'l NErwoR/rao fof/manso asc/1. LA Tan 1L Sept. 9, 1952 D. LEED 2,610,297

AUTOMATIC FREQUENCY CONTROIJ CIRCUIT l 5 sheets-sheet 2 By Qnmgm Sept. 9, 1952 D. LEED 2,610,297

AUTOMATIC FREQUENCY CONTROL CIRCUIT Filed D60. 14, 1948 5 Sheets-Sheet 5 /5 NF /3 N (Fu J F w3 f w, f

NuLr N/xm f F/G. /2 mf 2/) I8] (/7 /2 xrAL com: j Fluss /s mea. also. MUL 71 05C. w,

Naf)

( f E E2 l:

REACTNCE Tuer ccr F +A f ,5] NF ,3) N(F+Af) F 9J {94 NuLr N/XER DEI y Nmf) F/G. /3

2/2 NO: f) /8/ [/7 /2 xTAL (6/ coNr mss also. Faso. also. NUL r osc.

REAcrANcf DELAY TUBE ccr a,

F +A f /Nl/EN To@ D. LEE@ A 7' TURA/EV Patented Sept. 9, 1952 AUTOMATIC FREQUENCY oONTnOL CIRCUIT Daniel Leed, New York, N. Y., assignor to Bell 'Telephone Laboratories, Incorporated, New York, N. Y., a corporation of New York Application December 14, 1948, Serial No. 65,130 1c Claims. (ci. 25o- 36) 'This l'inventionrelates to automatic frequency control circuits, fand more specifically to such 'circuitsfin which the frequency'of a controllable oscillator is maintained at a predetermined'iixed diiference from a reference frequency.

Hyeretoforeinthe .prior art, frequency control Ycircuits embodyingffrequency discriminators have rbeen utilized'tocontrol the frequency of a controllable oscillator.

Such Ydiscriminators were able to -effect'control withinfa few cycles ofthe desired `predetermined frequency difference but vwere not capable ofeifecting control to the exact predeterminedfrequency difference. One illustration of such prior art circuit, of which there Yare-many, is'fcundin the patent of S. W. Seeley No. 2,121,103, issued June '21, 1938. Also, in the prior art automatic frequency control circuits including phase discriminators have been employed to maintain a -controllable oscillator at a fixed frequency'difference from -a reference frequency. Thesecircu-its enabled ian exact frequency control but-permitted lock-in at either a lower-or upper sidebandeither sideband being possible in a given circuit. Illustration of such circuits are in the patent of F. Pomyercyno. 2,288,025, issued June 30, 1942,a'nd in the patent of F. R. Dennis and E PLFel'ch, Jr., No. 2,369,663, issued February 20, 1945. It was found in the prior art circuits that the use of a 4phasevdiscrirninator alone not only presentedthe difficulty yof frequency lock-in at `the desired -sideband, but alsotended to lpresent the furtherdifculty of permitting severe Oscillation inthe automatic control circuit after synchronization had been completed at one or the other of Lthe two'possible sideban-ds, resulting 1n frequency 'modulation of the controlled oscilla-u Y tion. -Both o'f these difficulties would appear -to be imputable to the phase delays present inthe automatic control circuit.

The present invention contemplates a frequency control Vcircui'i-,in which the frequency of an oscillator'istlockedin at an exact predetermined difference relative -to a reference frequency including `a positive `'preselection of v the sideband atWl-iich the Vlock-in is effected.

Thema'in object ofthe invention is to maintain the frequency of the output voltage of an oscillator at an exact predetermined difference from the 4frequency of a reference voltage.

Another Objectis to preselect the sidcband at W-h-ichfrequency lock-in is effected.

Afurther object is to preclude extraneous oscillation in laY phase sensitive loop utilized for locking in two alternating voltages at a nxed predetermined frequency Vdiiierence therebetween.

Another object is to stabilize a frequency control circuit which includesy a phase sensitive loop.

In aV specific embodiment the invention com prises an oscillator and a vsource of reference frem quency between the frequencies Aof which an exact predetermined' difference is to be maintained, a generator of constant frequency, a phase discriminator for producing a potential-proportional to change of the relative phase of the constant frequency and the frequency of a portion of a component derivedfrom the waves of the oscillator and reference source, a frequency discriminator for producing from a further portion of the last-mentioned component a volt-age in accordance with la derivative of the last-mentioned phase change, andreactive means for connecting the outputs of the phase and frequency discriminators to the controlled. oscillator, fthe 'two discrminator output voltages being translated by the reactive means into corresponding changes in the effective reactance thereof whereby the oscilla-- tor is controlled to maintain the exact predetermined frequency diiference from the reference frequency. In an alternate embodiment, the frequency of an oscillator may be maintained exactly equal to the frequency of a reference voltage so that the predetermined frequency vdifference therebetween .is Zero.

A feature of theinventioninvolves ythe use of a voltage which is the derivative of the change of relative phasev between two alternating voltages for instantaneously effecting frequency correction in the controlled oscillator in response to a change of Yfrequencyin the reference voltage or to a change of controlled oscillator circuit constants caused, for example, by temperature drifts. Another feature concerns the use of such deriva- -tive voltage for stabilizing the lock-in of the con-- trolled oscillator at a desired sideband, i. e., at the'upper or lower sideband. the present invention, the derivative voltage servesto stabilize the controlled Oscillator atthe upper sideband. In bringing about such stabilization the derivative voltage tends to preclude extraneous oscillation in 'the loop including the phase discriminator. Another feature relatesto the use of such vderivative vvoltage for suppressing the unwanted sideband. A further feature involves theruse of a voltage proportional to the change of relative phase between two alternating voltages, together with theabove-noted derivative voltagefor maintaining the frequency of a controllable oscillator at a predetermined difference from the frequency of a reference voltage.

The invention will be readily understood from In `the instance of the following description when taken together with the accompanying drawings in which:

Fig. 1 is a box diagram illustrating a specic embodiment of the invention;

Fig. 2 is a schematic circuit of the two reactance tubes and controllable oscillator of Fig. 1;

Fig. 3 is a characteristic of the two reactance tubes and the controlled oscillator of Figs. l and 2;

Fig. 4 is a schematic circuit of the frequency discriminator of Fig. 1;

Fig. 5 is a characteristic of the frequency discriminator of Figs. 1 and 5;

Fig. 6 is a schematic circuit of the phase discriminator of Fig. l; Y

Fig. 7 is a characteristic of the phase discriminator of Figs. 1 and 6;

Figs. 8 and 9 are vector diagrams illustrating the principles of operation of the phase discriminatorl of Figs. 1 and 6;

Fig. l is a family of characteristics illustrating certain action in the frequency and phase discrirninators of Figs. 1, 4 and 6;

Fig. 11 is a family of vector diagrams illustrating certain action in Fig. 1;

Fig. 12 is a box diagram representing the circuit of Fig. 1 functioning as a one-mesh frequency servo-mechanism; and

Fig. 13 is a box diagram representing the circuit of Fig. 1 functioning as a one-mesh phase servo-mechanism.

Referring to Fig. 1 a controllable oscillator I0 has its frequency maintained at a fixed difference AF from an input voltage having a reference frequency F so that the output voltage of oscillator Ill has a frequency F-l-Af, for example, in a manner that will now be explained. A portion of the output voltage of oscillator I0 of frequency F-I-Af is supplied through a buffer amplifier II to a frequency multiplier I2 whose output is supplied to one input of mixer I3. The input voltage of reference frequency F' is applied through amplifier I4 and multiplier I5 to a second input of mixer I3. The mixer I3 and multipliers I2 and I utilize well-known designs, the multipliers serving to multiply the frequencies of the voltages applied thereto an integral number of times N which is three for the present description as will be hereinafter mentioned, and as disclosed in the patent of F. R. Dennis-E. P. Felch, Jr., supra.

The plate-to-ground capacity in the output of mixer I3, or other suitable filtering arrangement therein, is such as to provide an adequate shunt for all modulation components except the modulation component having a frequency N(Af) which is applied to the input of amplifier I6. After amplification, portions of the N(Af) component are applied to the inputs of frequency discriminator I1 and phase discriminator I8 whose outputs activate reactance tubes I 9 and 2U, respectively, whereby the frequency of oscillator Il! is controlled.

A crystal-controlled oscillator 2I of conventional design generates a voltage having a constant frequency equal to the N(Af) frequency of the modulation component supplied to the inputs of frequency and phase discriminators I'I and I8. The voltage of oscillator 2I is supplied through amplifier 22 to the second input of phase discriminator I8. A cathode-ray oscilloscope 23 has one horizontal plate connectedV to the output of amplifier 22 and is thereby energized by the N (Af) voltage of crystal-controlled Oscillator 2I and a vertical plate connected to the output of amplifier I6 and is thereby energized by the N(Af) component selected from the output of mixer I3. These two N(Af) voltages are compared by a Lissajous figure shown on the screen of oscilloscope 23 so that when the two voltages are in synchronism the Lissajous figure assumes the form of an ellipse as is well known in the art.

Fig. 2 shows with more circuit details the connection of the reactance tubes I9 and 20, Fig. 1, to the controlled oscillator I0. A network 3G is connected between the plate and control grid of oscillation tube 3I of the controlled oscillator I0, i. e., in the main feedbackY paths of oscillation tube 3|, and is proportioned to provide a total phase shift of 180 degrees between its input and output terminals for a voltage having the reference frequency F. The network 30 consists of two symmetrical 1r sections of condensers and inductance in cascade, each 1r section having a phase shift of degrees. The voltage at the mid-point 30a of the network 30 is accordingly 90 degrees out of phase with the voltages at the end terminals thereof. Hence, the `network 30 functions as a frequency-determining means for controlling the oscillations of oscillation tube 3l, the phase shifting network 30 being connected in the feedback loop of oscillation tube 3| As a consequence, the connection of the plates of reactance tubes I9 Yand 20 to the plate of oscillation tube 3I establishes a reactive impedance between the plate and ground of the latter tube when the control grids of the reactance tubes I9 and 20 are alternating current coupled by condensers 32 and 33, respectively, to the mid-point of the network 30 as shown in Fig. 2.

The effective reactance of the reactance tubes I9 and 20 at a given instant serves to introduce variable reactance into the phase-shifting network 38 and thereby control the frequency of oscillation of oscillation tube 3|, as determined by the transconductance of the reactance tubes I9 and 20, at the given instant. Variations of the bias applied to the control grids of the reactance tubes I 9 and 2G will control the transconductance of the latter tubes. This is more fully disclosed in the copending application of F. R. Dennis, Serial No. 736,437, filed March 22, 1947, now Patent No. 2,486,265, issued October 25, 1949. The frequency of the controlled oscillator I0 can therefore be varied by changing the bias on the control grids of the reactance tubes I9 and 20. Resistance 34 constitutes a termination for network 30 at the output terminals thereof. Networks 35 and 36 serve to decouple, from the power sources, the filament and plate circuits, respectively, of the oscillation tube 3 I.

To minimize the degenerative effect of varying cathode voltage when the transconductance of reactance tubes I9 and 20 is being varied by changes of grid bias due to the operation of frequency and phase discriminators I 'I and I8, respectively, as will be hereinafter pointed out, a xed amount of biasing current is supplied to cathode resistors 31 and 38, Fig. 2, through resistors 39 and 40, respectively.

The control of the oscillation frequency of oscillation tube 3I by the reactance tubes in a broad sense is well known. Both reactance tubes I9 and 20 together with controlled oscillator I0, have a characteristic, forl example, as that shown in Fig. 3.

The frequency discriminator I1 in box form in Fig. 1 is shown in detail in the schematic cirpacitance -of- .condensers 5. Y cuit .of 4 wherein theelec'tronic amplifier I6 isithe electronic amplifier with .thefsame reference .numeral [in Figi .1." :C'ondensers .II2k and' 43 possess negligible [impedance over the frequency band .off the .discriminator ITI, and. the inductance L possesses ahigh impedance over this Yfrequency Vband. The `self-inductance ofthe secondary windingof transformer 44 and the ca- 45 and 46 are resonant to voltage having the frequency. N(Af). "Resistances 41 and 48 provide an electrical center with respect to the voltage across condensers VI5,and 46. With reference to the junction point ',49`of resistances `4;'I- and y43, .currents-of equal `magnitudes but .opposite phase flow'through the ,latter resistanees. The voltages acrossresistances 4l and-Mare substantially in quadrature with the constant alternating rplate current of: pentode amplifier I6. Y

This is seen to be so when it is realized that,

assuming transformen to be ideal, the constant-v plate current forced into the primary winding of transformer 'M produces'a constant current ofxopposit'e Aphase .in .the secondary winding :of this 'transformer'. 'Thezlatter l.current'then develops :a potential across the parallel. combinationpf'zcondensers 4.5;;and 46 andv resistances 4! and 48. .Over ithe Vfrequency band of' frequency discriminator yIi"I, Aliigsxl ande, the impedance of Vthe above-identified parallel .combinationv of condensers :and :resistances is Ypractically entirely capacitative; and. .the `potential Ydeveloped across the combination `'is therefore substantially in quadrature N,with fthefcurrent in the secondary winding 'of' transformer-.44; and, `in View of the indicatedfl phase relation between the primary and '.secondarytwindings *of transformer 44, the potential across the Aalsove-identiiied `parallel combination `of condensers and resistances is in quadrature with the i'current in the primary Winding 'of transformer '44. f

As transformer Mis assumedto be ideal, the impedance presented Vby frequency discriminator I'I-toztheplate ofel'ectronicamplier Iis equal to the impedance -of 'primary winding of transformer k:IIlI'plus the impedance coupled 'into the primaryvwinding from its secondary circuit. It

may be readily shown that such .impedance is substantially resistive atv the'. frequency to which the secondary .Winding of transie'rrner d'is tuned, the latter winding being tuned to the frequency N(Af) as hereinbefore mentioned. Y The alterhating-current plate voltage of amplifier IE 'injected ,at the mid-point 49 isinphase with the plate current lo'f the electronic amplierI .and

such decrease. The mode of operation of the frequency"discriminatorll is such as illustrated bythe characteristic shownin Fig. whereby lock-,in of the controlled'oscillator IIl is effected at'jthe upper sideband F-i-"Af as above mentioned. This operation is wellknown in the art, one exemplication 'beingdisclosed in the patent of S. W.S'eeley,.supra.

The .phasediscriminator IB in ig.I -1 is shown in `detail in .theschematc circuit of Fig. 6 Wherein the electronic .amplifiers I6 and 22 are identicalr with the amplifiers .having the same reference numerals in Fig. 1.. The phase discriminator IBin Fig. '6 includes a pair of electronic diode rectifiers .55.and 56 whose plates are directly connected .to the split secondary .winding of an in- Y put transformer 51 which has its primary Winding .connected -to amplifier 22 and thereby to crystal-controlled oscillator 2 I, Fig.. 1. The cathodesof `rdioderectiersv and''r are connected across.aseriallyconnected pair of resistances 58 andl59 ,whosecornmon pointll is connected to therefore inquadrature ywith the voltage across Y resistances 41 andes so that'the sum of the rectiiiedL voltages added in opposition and effective across output condenser l52 is Zero;

Deviations above or'below the frequency Nmf) cause'the impedance presented by the frequency discriminator `II'to thev plate or amplifier I6' to become inductive -orv 'capacitative depending on -the sense ofthe deviation.- "Hence, the potential across fthe' `output condenser '52 4will have a magfrequency of the'voltage" applied through ampli` fier `vI5 is above or`below the frequency`N(Af). For V`the purpose of this illustration, the voltage across condenser 52 will have a polarityfor a frequency increase above the frequency N(Af) and a magnitude dependent on the amount of such increase, and will have a polarity for a frequency decrease below the frequency N(Af) and a magnitude depending on the vamount of nitude m,and polarity A'depending on whether'the one terminalof a seccndarywinding of an input transformer 6I, the opposite terminal of this secondary Winding being connected to the lmidpoint of the secondary winding of input transformer .51. v'Iheprimary winding-of input transformer'l `is connected-to the output of amplifier leand thereby .to the output of lmixer I3, Fig. 1. Acrossthe-pair of resistors 58 and 5S are connected in parallel a condenser E2-and a poten.-

tiometer 63. AA condenser 64 connects .thefpotentiometer slider to ground for filtering purposes. The phase discriminator I8 has acharacteristic as shown in Fig. 7.

The phase discriminator I8 in Fig. 6 functions substantially as a phase detector as follows: Let it be assumed that the transformers 51 .and 6I have unity ratio, and the voltage e1=E`1 sin (wm-9) and the voltage e2=E2 sin (wt). Then the voltage output of phase discriminator I3, i. e., the voltage across condenser .62, is proportional tothe arithmetical difference, if any, between the envelopes of Ythe -total .alternating-current vvoltages applied to the diode rectiers 55 and 56.y Let it be further assumed that a quadrature phase relation occurs initially between the voltages e1 and ez so that the-phase, 0, of one voltage differs from that lof the other by an odd multiple of degrees. Then,1'the arithnietical difference between the envelopes of the alternating-current voltages applied to the diode rectiers 55 and 56 shouldV be zero whereby` avoltage of zero magnitude is caused to occur across condenser S2. rI'his may be readily seen by reference to vector relationships shown in Fig.v 8 wherein the resultants OA and OB are substantially equal, these resultants representing the peak 'alternatingcurrent voltages applied to the diode rectifiers 55 and 56, respectively. As a consequence, following rectification of the alternating-current voltages represented by OA and OB, nov difference occurs between the voltages .across resistances 58 and 59, and the voltage across condenser 62 is zero. Hence, the phase discriminator I8 maybe operating at either point of its characteristic shown in Fig. 7.

Now, let it be assumed that 'a change of phase 'occurs between the voltages e1 and ve2 so that the phase difference @is no longer an odd multiple of 90 degrees. As a consequence, a difference will occur between the resultant total alternat- 7 ing-current voltages applied to the `diode rectiers 55 and 56, and therefore between the rectied voltages across resistances 58 and 59. The arithmetical difference between these voltages will be reflected as a voltage on condenser 62 in Fig. 6 with a polarity which willv be presently identified. This will be evident from the vector relationships n Fig. 9, constructed for the'case in which is less than 90 degrees wherein the resultant OA is larger than the resultant OB, these resultants representing Vthe amplitudes of the total alternating-current voltages applied to the diode rectiers 55 and 56, respectively; In view of the above, the point 65 is negative with respect to ground whereb-y the voltage on condenser 62 has a negative polarity, and the phase discriminator I8 is operating, for example, atV

a point X on its characteristic shown in Fig. '7. Where the resultant O'B becomes larger than the resultant O'A in Fig. 9, 'then the point V65 in Fig. 6 would be positive with respect to ground thereby placing a positive charge on condenser 62 to an extent depending on the arithmetical difference between the latter two resultants. Hence, the phase discriminator yI8 would be operating, for example, at a point Y on its characteristic shown in Fig. '7. For 0 angles greater than 180 degrees the variation of the voltage across condenser 62 follows the negative slope of the characteristic in Fig. 7. The operation of the phase discriminator I8 in proximity of point of its characteristic in Fg. '7 favors the upper sideband whereas the operation in proximity of thepoint l slr favors the lower sideband. This type of phase discriminator or phase detector is essentially disclosed in the patent of A. F. Pomeroy, supra.

The vectorial representations shown in Figs. S and 9 may be solved as follows: `As previously mentioned in connection with a change of phase, relative to 90 degrees, between voltages e1 and e2 in Fig. 6, it was assumed that,`

To simplify the vector analysis of Fig. 6 as represented in Fig. 9, it will be further assumed that Then, from the law of cosines, the total alterhating-current voltage applied to'rectiiier 55 in Fig. 6 is OA'=\/E2+E2l-2E2 cos 6 and the total alternating-current voltage applied to rectifier 56 in Fig. 6 is :2E (cos g-sin Therefore, the phase discriminator I8 has the characteristic shown in Fig. '7 as above stated. As plotted from empirical data, the characteristic curve of Fig. '7 was found to possess substantially linear ranges for 0 angles greater than 30 degrees but less than 150 degrees, and greater than 210 degrees but less thanY 330 degrees. Hence, over such ranges of the characteristic curve inFig. '7, it may be assumed that the voltage across condenser 62 in Fig. 6 is that is, a linear relationship between Ecsz and 9, where m and b are constants, m'being the slope of the aforementioned linear portions of the characteristic curve in Fig. '7 and b the intercept of the latter slope on the Y axis. Referring to Fig. '7, it will be observed that the slopes m of the two curves are substantially centered at The circuit of Fig, l operates to effect two controlling operations, viz: (1) to establish the output voltage of the controlledloscillator ID at the predetermined frequencyr F-I-Af for an input voltage having a reference frequency F, and (l2) to maintain such voltage precisely at the latter frequency regardless of changes in the reference frequency F of the input voltage F or in the frequency determining circuit constants of oscillator I0, in la manner that will be presently explained. Let it be initially assumed for the purpose of this explanation that the circuit of Fig. 1 is adjusted to a steady state condition in which an input voltage has a reference frequency F 15 mega-cycles) and that the output voltage of the controlled oscillator IU is to be maintained at the frequency F-I-Af (15 megacycles-I-Sl kilocycles) As a consequence, mixer I3 has applied to the input thereof, (l) a rst voltage having the frequency 3F (45 megacycles) from the output ofr multiplier I 5, and (2) a second voltage having the frequency N FIAf) or 3(15 megacycles-l-Sl kilocycles) or 45 megacycles-i-SS kilocycles from the output of multiplier I2. It is therefore apparent that the multipliers I 2 and I 5 function as frequency triplers whereby the term N in each of the expressions NF and N (F4-Af) has the numerical value 3. As previously mentioned, this multiplication is disclosed in the patent of F. R. Dennis-E. P. Felch, Jr., supra.

The voltage selected from the output of mixer I3 and applied through amplifier I 6 to the inputs of frequency and phase discriminators I1 and I8, respectively, has the frequency N Af) or 93 kilocycles. The comparison voltage supplied Vfrom the crystal-controlled oscillator 2l throughl amplier 22 to a second input of phase discriminator I8 also has the frequency NAf) or 93 kilocycles. A no-voltage charge is present on condenser 52 of the frequency discriminatoi` I1 in Fig. 4 so that the latter is operating at the point N(Af) on its characteristic in Fig. 5; and by adjustment of frequency determining condenser 3 Ia of controlled oscillator l0 in Fig. 2 the phase difference between the above-mentioned Vinputs to phase discriminator I8 is 90'degrees, so that a no-voltage charge is present on the condenser 62 of the phase discriminator I8 in- Fig. 6 and operation is at the point on the phase discriminator characteristic in Fig. 7. Finally, with the above assumed conditions .has changed from a re aarden? For the purpose of' 'subsequent explanation,

` vunder the initiany assumed steady state condition in Fig. 1, it will be understood: 1, thatv such steady state condition has persisted for a sufficient time duration that all transients due toa previous 4 change in the reference frequency F of the input voltage have decayedto' zero; 2, that'beforerany change takes place in the reference frequency F, the input voltage has the reference frequency F, and the voltage output of the controlledloscillator I has the frequency Ill-Af; 3, that by amanipulation of a frequency-controlling condenser 31a inthe controlled oscillator ID, Fig. 2, the operating Y strain on the circuit. of Fig. 1 was reduced substantiallyA to zero as noted' above; 4, that, asa

consequence of the foregoing, the operating condition of thev circuit of Fig. l at' the initial time t='-0 isiillustrated by the points 0, 2, 6. and r1in the characteristic curves A, B, C and D, respectively, of Fig.`; vand 5, that no circuit delays are present in Fig. 1 except a virtual delay introduced by the feature of' integration'in the phase sensitive loop asvvill be pointed out. later herein.

Y It'will be further understood that, the curves in Figs. 10A, 10B, 10C andv 10D are identical with the curves in Figs. 5, '7 and 3, respectively, the family of curves in Fig. 10 being for theypurpose of facilitating visual inspectionof certain action in Fig. 1.`

` Now, let, it be assumed that theinput voltage Vference frequency F to a new reference frequency F+Af1. As a consehave the frequency N (F4-Ati), andthe voltage selected from the output of rnixer`l3V and applied through amplifiery I6 to the frequency discriminator 'I1 has a frequency 01 N (Af-fAfi) :Afa Y N(Afi) occurs in the voltage'applied tothe input of frequency discriminator II'I. Thusfanno error of phase has developed atthe phase discriminator `I8 loetv'veen'the two-voltage inputsY having the frequencies of NM2?)A and Afa Hence,v at the instant of the rchange of'theinput voltage from frequency F to frequency criminator I8 exerts no correctiveforce on the controlled oscillatorV I0, and for the moment may be deemed to be inoperative; but at the same time, however, the, frequency discrirninator I7 is operative to effect its full corrective force .in` a. manner that will be presently Y. explained. The latter `force serves to increase the frequency of the output'voliiage of the controlled oscillator Ill by an amount depending upon fthe effective galn of the frequency loop,i..e., the loop including frequency discriminator I1, reactance tube I9, oscillator I0,amplifler IIm-ultiplier I2, mixer I3, Iand amplifier; I6. In the `embodiment described, thisfrequency loop has a gainof 30, and it 1s therefore effective at the time 'tu negligibly soon `following t=0, to cutthe initial frequency error NMA) 'substantially to one-thirtiethrthereofjbefore the phase discriminator. I8 commencesto exert its corrective force in. amanner .to beex- -plained hereinafter.

Theforegoing Vvvillbe cleareliwfrorn a consideration ofthek 1ical values-"assigned 'for the purpose of thisjexplanationrErr this connection,

there isassumed ya change Afl A(1 ln-locycle') in F+Af1, the .phase dis- I ifo the frequency-F of thel input voltage. Hence, the input voltage will-be assumed to have Ya new reference frequency F-{eAfi `or 15megacycles-If1 kilocycle. From this, the output voltage of multiplier I5 will have the frequency N(F-I.Af1) or Li5 megacycles-l-B klocycles andy the voltage .selected from the output of the mixeri13 and applied through amplifier' I5 to the inputs ofy the frequencyl and phase discriminators I'I and I8 willhave the frequency N (F-leAl-N (FPi-Afl) or Afz', i. e., f Y

or thefrequenxnf.v Afa of 9.0 kilo'cycles. riihus, a frequencyv error of N (Afr) or 3 kilocyclesA will occur in the voltage. applied to theinput ofl frequency discriininaltor` IIg., Due to the gain 3Q of the above-traced. frequency loop, the initial error, Nmfl), of Bkilocyclesfis reducedsubstantially to one-thirtieth thereof, i. e. to 100 cycles (3,000 1/0). According1y,the assumed new 0D'- erating condition of Fig. 1 at the instant t1, i. e., immediately followingv the corrective effect of Afre-- quency discriminator II,. may be represented by the point. 1 in Fig. 10A.; thelpoi'nt/ 2j inFig'. 10B but commencing44 to; move upwardly; the point'f butcommencing to move rightwardly in Fig. 10C,

' and the point 8 in Fig. 10D.

At the instant t1', the phase of thegvol-tage produced by the crystal-controlled. oscillator 2iape pliedto phaseA discrimination IB'through amplifier' 22, and having thefrequency N(Af),cr glkilocycles, tends; ,togadvance with lreference to the phase of; the voltage having the frequency of 93 kilocycles-lOD cycles, the lat-ter Vbeing applied fromy the output of amplifier i5 toY .thephase discriminatorie. Y This may be readilyillustrated from;4 theY vector Arelationslfiips,:shown in Fig. 11. The horizontalvector of zero phase in Fig'. 11A

- represents4 the voltage `having frequencyvv of 93'kilocycles- 1OQ cycles in the output of ampliiier I6 and supplied to the inputs of'frequency diserirninator Iv'lafnd phase discriminator i8 at the instant t1, immediately following rthecoarse correction `effectedlnv the frequency discriminator I1, i. e. atgthe instant when the rphase discrimif nator I8 commences to exert the fine correction that will now be explained.r The vertical vector shown in Fig. 11B represents the voltage. having frequency 93 kilocycles in the output'ofV amplifier 22, the Vector in Fig. liB being degrees (e2-0.1:9u degrees) ahead of the' vector in Fig. 11A as a result of previously indicated initial conditionsv (3) and (e).` Thus, the? vector in Fig. 11A is moving at a velocity corresponding to the frequency "of 33kilocycles-1OO cycles while the vector in FigilB is movingata velocity corresponding exactly to the frequency of. 93 kilocycles. Y

The combined effect of the frequency and phase discriminator's Il and I8, respectively, is ultimately to increasethe velocity ofthe vector (93 kilocycles-l() cycles) in Fig; 11A until it exactly equals the velocity of" the vVecter (93 kilocycles) in 11B but ynot necessarily to reestablish the vvinitial?" phase relative thereof.

Obviously, the vconstant frequency 'vector #in a Fig. 11B will travel: agreater angular..r distance former. :Inzviewof the. difference vbetween the.

velocities of the tworvectors, the phase difference between the voltages present in the outputs of amplifiers 22 and I6 vand supplied as inputs to phase discriminator I8 tends to increase whereby a positive voltage tending to increase correspondingly is developed in the output of phase discriminator I8. This Voltage applied to' reactance tube tends to increase the frequency of oscillation of oscillation tube 3|, Fig. 2, and thereby the frequency of the output voltage of the controlled oscillator IG as shown in Fig. 10C. This tends further to reduce to less than 100 cycles the frequency error in the voltage inputs to both frequency and phase discriminators l'i and I8.

At the intermediate instant t2, i. e., after the phase discriminator I3 has commenced to exert its corrective force by means of its control over reactance tube 20, the vector of the voltage in the output of amplifier I6 will occupy, for example, the position shown in Fig. 11C having the angle 01 with reference to its initial position shown in Fig. 11A. At the same time the vector of the crystal-controlled voltage in the output of amplifier 22 will occupy, for example, the position shown in Fig. 11D and have the angle 02 in the latter figure. Bearing in mind that the velocity of the vector in Fig. 11D is greater than that of the vector in Fig. 11C as above mentioned, it will be obvious that the angular difference between the vectors in Figs. 11D and 11C will tend to increase to the relation of 90 degrees +A0, the term A6 representing the angular advance of the Vector in Fig. 11D over that in Fig. 11C at the time tz. Therefore, in Figs. 11D and 11C, 9i-01:90 degrees-|-A0. In this connection, it will'be obvious that the phase difference between the vectors in Figs. 11D and 11C has increased beyond what it was in Figs. 11A and 11B. The positive voltage developed in the output of phase discriminator i8 and applied from condenser 62 in Fig. 6 to reactance tube 20 in Fig. 2 tends further to increase the frequency of oscillation of oscillation tube 3l and thereby the frequency of the output voltage of the controlled oscillator l in Fig. l. Due to increased frequency, the velocity of voltage vector in Fig. 11C will tend to increase with advancing time, thereby tending to diminish the-rate of growth of the angular advance A0 of the vector in Fig. 11D thereover. time t2 in Figs. 11C and 11D, i. e. at an intermediate instant of correction by the phase discriminator I 8, the term A0 increases, but at a decreasing rate of growth.

As the new steady state condition in Fig 1 is Hence, at the approached and the need for frequency ccrrection becomes lessracute, the rate of progression along the curve in Fig. 10B decreases until the operation of Fig. 1 nally stabilizes at the time t3 in Figs. 11E and 11F of complete correction in proximity of point 4 in Fig. 10B. Thus, the vector of the voltage in the output of amplifier I6 in Fig. 1 Will occupy, for example, the position v shown in Fig. 11E having the angle 01 with refer- 2l through amplifier 22; that due to identical frequencies, the velocity of, the vectors in Figs. 11E and 11F vwillbe thesame; 'and thatitheangular advance A0 Vofthe''vector`in.`lig.zl 1F 'over' the vector in Fig. llEhas reachedthe point beyond which 'further4 reduction cannotjbe leiected', the term A0 now having;substantiallyba': constant value. With the correction cpmpletedf as'slhown in Figs. 11E and 11F;neel-90rdegreesa-fn) 1. The term'(A0)1 is thenal angular ladvance of the vector, Fig; 11F,Vv representing the voltage of the crystal-controlled oscillatorj2 Iv overY the vector, Fig. 11E, representing thejvoltage inthe output of' amplifier I6v 'during' the time'interval required to restore the frequency of ,theV controlled oscillator l0 to the F-i-Af value, in response to the assumed l-kilocycle change inthe reference frequency F of the input voltagefin Fig.. 1 mentioned previously.. :In this 'connectionitjwill be understood that the phase difference between'the vectors in Figs.` 11F and, 11E remainsconstant but increased over' what it'was in Figs.` 11B and 11A. As will be mentioned hereinafter, the frequency difference VAj may also be zero. .l The new steady stateV operating condition of Fig; lmaybe represented by (a) the point 0 in Fig.1GA,:since the voltage output of amplifier It hasthe frequency N(Af) or 93 kilocycles at theV conclusion of the correction; (b) the point 7 in Fig.j10D because the point 0 in Fig. lOAcauses a return to the former point; (c) at thepoint 4, Fig, 10B; and (d) the point'in Fig. 10C,.the two next preceding itemsV (c) and (d) being Ldue tothe Vterm (MM explained hereinbeforefin.connection with Fig. 6. For a Adecrease in reference Fof the input voltage in Fig. l, an opposite action takes place.

It will be understood that the frequency and phase discriminators land I8, shown in Figs. 4 and 6, respectively, Aand the controlled oscillator shown in Fig. 2 were selectedfor, the purpose of illustrating the invention; and thatj other frequency and phase` discriminator types and means 1for controltllilng titre frequency Yof .an foscillator :nown 1n e ar ma rb alte n in Fig. 1. l y e r ately employed In analyzing the operation of theover-all controlled oscillator circuit in Fig.Y 1', the latter may be viewed as an electronic servo-mechanism. Y As 1s' wel1.known, the function of. ya servomechanism is to control anfoutput quantity s0 that it invariably bears some fixed relationV to an "1nputror reference quantity; This is accomplished by controlling'the output `according to some function of the deviation from the specic relation between input and Youtput which it is desired to maintain. This-deviation is called the system error.'V In the case of a simple mechanical remote positional` control lservo the error is frequently the-difference be'tween the angular settings of a local Vand a remo'tely'located shaft. This error, or difference between: the two shaft angles is translated by somemethod of conversion to corresponding electrical'.'voltagewhich actuates a motor controlling theY pc'sition of the remotely located' shaft in such '-a fashion/that the error tends to be annihilated.` This type of control has been called closed-cycle,'because the angle of the output shaft of the -controller, or motor, is compared with that of the input shaft and the product of this comparison is then used to energize the motor. Y'

All of the elements of a servoemechanism may be recognized in the circuit of ,Fig. 1.- 0The input may be considered the frequency F, and the output, the frequency of controlled oscillator l0. The relation to be maintainedrbetween'input and output is not equality, as in the above mechanical g the error is F1-(F+Af).

plication stages l2 `and I5 in the circuit of Fig. 1 the reactance Vtubes I9 vand 20, or servo con-A trollers are actuated by functions of s s N. F1- F+Af where N is the multiplication factor and there- Y fore in subsequent discussion the latter quantity will more conveniently be referred toas the system error. The error converters or translators are the frequency discriminator rl 1 and phaser discriminator |73 whichvtranslate the frequencyerrer to voltages adaptable 'for controlling the frequency of oscillator means afforded by the rea'cta'nc'e tubes ISiy andil.

In an alternative view, the regulated quantity can be taken tobe the phase of the output voltage of controlled oscillator I0. As frequency and phase are integrally related, a control of one implies control of the other. As is well known in the electrical art, A)a wave of. varying frequency may be 'presented by' avctbr rotaungfabout a. central point,l Fig. length, if the wave is nrhodulated in amplitude and traversing between two instants of time an angle which is proportional to the time integral of the instantaneous frequency. The position of suchvector at some instant in relation to a reference line intersectngthe axis ofrotation is the instantaneous phasej or merely phase. Obviously, then, when phase is under control, its derivative instantaneous frequency or merely frequency isimplicitly controlled, and vice versa.

Accordingly, the controlled; oscillator circuit Fig. l may be considered (l) a frequency servomechanism, ori (2;) a phase servo-mechanism. In 'the consideration' as a frequency servofmecha- Ynisirn, it will be subsequently demonstrated that such -frequency servo-mechanism, toa first. degrecA of approximation, belongs in that class of servo-mechanisms in which the correcting force for controlling the output of themechanism 1s actuated by voltage data .proportional to frequencyerror plus time integralof frequency error, or what is often called proportional plus integral control. Such control is so des1gnated Transientsl in Linear Systems, by

Messrs. M. F. Gardner and :.l. L. VBarnes (John Wiley `and Sons, 19425,'.page 194. I n the consideraticn .as Y a phase servo-mechanism, 1t will be 'also demonstrated.hereinafterthat such p hase servo-mechanism,to 'a first degree of approximation, belongs to theclass of servofmechanisms in 65 'which the 'correcting force .for controlling the output of 'the mechanism i'senergized by voltage data 'proportional to lphase 'error plus the time Vderivative ofphase'error.

-I-nthecer-isideration as a frequency servom mechanism, theY presence .of the integral 'comp'onent presently to be demonstrated insures that 'thesteadystateerrors'reduced to zero. This is weufxawa nr fue anni servo--meciranisms.v 1f

den increment in the magnitude of the input ID` through the reactive' Because of the multij c, T14 quantity,

Iijand the linear component directly proportional tofrequency error is'suppl'ied1 by the frequency discriminator vIl.

n this connection it will nowbefdemonstrated that the phase discriminator l8'produces an output voltage `which is instantaneously proportional over the linear ranges. of its characteristic, as discussed above regarding Figs. 6 and 7, to ,the time integral of frequency erro'r,-i. e., to the time integral of the instantaneous frequency :difference between the two inputs Vtothe phase discriminator le. outputvol'tage supplied vby the vphase discriminator Ieresults from the envelope detection fof the twol voltages applied to the diodes and 5S, thereof. criminator circuit of Fig. 6 includes a filter composed of resistances 58 and 59, potentiometer 63 and condensers B2 and 64, a finite time constant of delay results therefrom, and determines a maximum rate of change of the voltage-envelopes .as applied to the diodes 55 and 56 of the phase discriminator I8 in Fig. 6, which can be followed. This implies a maximum rateof change of phase between the inputs to which the output filter can respond, and thereby restricts the range of time varying frequency difference to which the phase discriminator I8 can respond as an integrator. This is the ancient problem Aof delay in servodemodulators. The integration concept herein therefore applies only when thephase differential between the two alternatingcurrent voltage in putsvto -the phase discrimina-tor i8 i's varying at a ratesloWer than a specific rate which is roughly computable from the lter constants.

As above pointed out, the steady state `characteristic of the phase discriminator I8, Fig. 6, is given bythe characteristic Ain Fig. .'1 `in which the slopes m are substantially centered atlpoints Now, let it be initially assumed rthat 'the voltages e1 and e2 in Fig. 6 have the same frequency but voltage e2 lags the voltage e1.; that thephase discriminatcr le is operating at the point and on its characteristic curve in Fig. '7; and that 'an output voltage E1 effective across the condenser `E2 is Zero. As a consequence, the phase-time relation between e1 and yc2 can be represented at a Ytions of the vectors in Figs. 111A and time instant tio by the yvectors in Figs. 11A and B which are rotating in a 'counter-clockwise direction. From a phase viewpoint, it is only necessary to consider the 'instantaneous -di'rec- Let it be assumed forrthis explanation that at the instant t=t1, both vectors :in Figs. V11A and B are in motion with an angular velocity occorresponding to thefrequency Thev integral component 1 As the phase dis-v Now let it be further assumed that the vector in Fig. 11B is suddenly accelerated, i. e., the frequency of voltage e1 in Fig. 6 is increased and has a velocity w1 (t) and that the frequency of voltage e2. is maintained at the velocity w2=w0. At the time t=t1, the vectors in Figs. 11A and B are 90 degrees out of phase, but during the next succeeding interval At, the vector velocity corresponding to frequency w1 is wo-I-Am where .M21 is the difference between the average velocity of wmf) and the velocity m2 during the interval At. Consequently, at the end of time Art, the vector in Fig. 11B will have 4moved through an increment of angle At(wo-I-AQ1), and the vector in Fig. 11A will have moved through, Aime). Now let it be assumed that at the instant t=t1+At, the frequency of thevector in Fig. 11B is returned to the velocity w1=wu lwhich is maintained for At seconds. Duringl the latter interval then, the velocity w1 equals the velocity wz, i. e., wi=w2 whereat the steady state condition prevails. But now the phase relationship between voltages e1 and e2 has changed because the angle of the vector in Fig. 11B has advanced a farther angular distance than didthe vector in Fig. 11A.

Therefore, the phase difference between the vectors in Figs. 11A and B during the first steady state interval is the angle of the vector in Fig. 11B and Aime) is the angle of the Vectorin Fig. 11A, and

where E1 is the output across condenser 62 in Fig. 6 during the first steady state interval and m is the linear slope in Fig. 7.

At` the instant tzti-I-Znt, the velocity of the vector in Fig. 11B is again increased to m4-A92, which is maintained for another interval At.' A92 represents the average velocity difference between the vectors during the interval between t=t1+2nt and t: tr-I-Bnt. At the instant tl-I-Snt, the velocity w1(t) of the vector in Fig. 11B is again returned to the velocity c1105) :wu for At seconds. During this second steady state interval, the difference between angles of the vectors in Figs. 11A and B where is the initial angle of the vector in Fig. 11B; At(w{-AS21) is the angular increment to the vector in Fig. 11B at the instant tz-.tl-I-At; At(wo-}AQ2) is the angular increment to the vector in Fig. 11B at the instant tztl-I-Snt; the first wont is the angular increment to the vector in Fig. 11A at the instant t-:tl-i-At; and the second wont is the angular increment to the vector in Fig. 11A at the instant t:t1-{3At; and

16 where E2 is the output'across condenser 62 in Fig. 6 during theesecond steady state interval; and m is the linear slope in Fig. 7.

For the nth interval Assuming new, vwithin an interval 0 t T,

locity differences Aile in passing to the limit. Also Y since Y a Y Amt) =21rAf(t) In Equations 1A and 1B, E05) y is the voltage output of the discriminator I8 in Figs. land 6,

.and is a function of Afd), the instantaneous frequency difference between the voltages e1 and e2 in Fig. 6.

Therefore, from Equation 1B where Ecezis the voltage across condenser 62 in Fig. 6, during a period of frequency correction.

Note that the foregoing integral relations apply only when the varying phase difference,

between er and e2, is confined to the substantially linear range of the phase discriminator characteristic in Fig. 7 wherein the slope m may be considered constant.

As it is convenient to think in terms of rotating vector analogue to electrical frequency, the instantaneous velocities w1, wz, w3, and 'm4 may be assumed to represent voltages in Fig. 1 having the frequencies N (Af) (crystal controlled oscillator 2I N(Af) (steady state output of amplifier I6 from Ythe mixer I3), NF (output of multiplier I5), and N (F-I-Af) (steady state output of multiplier I2) respectively.

From Equation 1A,

the phase discriminator I8 output voltage.

Therefore,

thus demonstratingthe integrating property of the phase discrimnator I 8.

It will now be shown that the frequency discriminator'II in Fig. 2 provides a voltage component actuating the reactance tube I9 which is directly proportional 'to frequency error. By adjustment of the capacitanc'es 45 and 46 in the frequency discriminator circuit I1 of Fig. 4, the center frequency of the latter discriminator, i. e., the input frequency to the discriminator for which zero control voltage is obtained at the discriminator I1 output, is made equal to the frequency corresponding to w1 of the above Equation 3. As shown in Fig. 5, the characteristic of the frequency discriminator I 1 is substantially linear between its maximum and minimum values andpossessesa slope a. Acoordinglmtlre'voltage output of the frequermyv d'scriminator I1 is Y l Eo-s2=,l(w1-jfwzi c constituting the controller voltage directly proportional to frequency 'error 'and actuating the reactance tube le, el and o2 are as defined above. Y f

' With respect to the frequency of the controlled oscillator I as the regulated parameter` of the electronic servomec'hanisrn, the frequency sensitive control loop, consistingo'f frequency discrimnator H, react'ance tube I9, amplifier 'I'Lni'ultiplier I2, mixer I3, amplifier I6 and oscillator l0 of Fig.- l provides proportional control by the Equation llabo've. Tnepha'se sensitive controlloop, comprising phase discriminator I 8,`reactano'e tube 20, amplifier Il, multiplier I2, mixer I3, amplifier I6, and oscillator In provides the integral control in accordance with Equation 3 above.

The system of combined phase and frequency sensitive control as shown in Fig. 1, possesses advantages not found in systems having phase or frequency sensitive control alone, as will be now pointed out. In a control circuit which uses only' a. phase discriminator and associated reactance tube, the controlled oscillator may lock in at either of two sideband. frequencies. These are F-l-Af, and F-A, in which F is the high frequency reference input to the circuit of Fig. l. Operation is at upper sideband when control is along the positive slope centered around of the phase dscriminator output voltage curve in Fig. 7, and at lower-sideband if control is along the negative'slope centered around Thus, an ambiguity of sideband exists, though the attribute of zero frequency error is' retained as shown in the Pomeroy patent, supra. When only a frequency discriminator and reactance tube are used, lock-in isv possibleat only one ofthe two sideband frequencies, determined by the poling of -the frequency discriminator output voltage. A frequency error, however, is present, which is 'essential to-the operation` of such a frequency sensitive control loop, as is well known in theart.

:Thata control circuit using only the phase discriminatortype ofcontrol is capable of lock-in ett-:either sideband'may be Seen from the following, In Fi g. lV the Ycol'ltrolled oscillator IG is maintained in upper sidebandrelatiomF24-Alito input frequency F, ,ancloperation' on the ,phase discriminator characteristic is therefore along the positive mk slope in Fig., 7 as noted above. Assume .now that the reactance tube IS in the heretoforetraced frequency sensitive loop is 'momentarily removed from the circuit so that onlyl-thejloop ini `fcluding the phase discriminatorqis'operative. vlf

the input frequency F is now slightlyincreased, this is reflected as a decrease in the frequency of ez in relation to e1 so that the phase of e1 advances over that of c2 and increasing corrective voltage isdevelopodat .the yphase discriminato-r I Soutput,ilas vindicated by. Fig. 7, raising. thefrelquency of controlled oscillatorvv le through the meansv of reafctance tube 25.0, 'v thus, eliminatingthenerron An opposite action occurs whenthe frequency F *is/,decreased With-the frequency sensitive control loop still inoperative, contro-lr on `the nega-f' 18 tive slope of *the* phase discriminator I8 occurs 'when 'the controlled oscillator I0 is in the lower sideband relation, F-Af, to input frequency F. Under the latter condition, lan increase to frequency F is reflected as an increase in the frequency 'of e2 in relation to el, so that the phaseof e1 slips behind' that of e'z 'causing the point of operation on the negative slope of the phase discriminato-r I8 characteristic in Fig. 'l to move upwardly, thus increasing the frequency of controlled oscillator AIll and leliminating the error. As` before, an. opposite action occurs if FF is decreased. `rI-lence, there are two modes of. control possible onthe positive, and negative m slopes of Fig. I7, only one of which is generally desirable in agiveri circuit. l l

e The frequency sensitive loop, including the f reqnency discriminatcr I1 is polarized for effecting synchronization, or frequency lock-in, at an upper or lower sideband, as desired, in a manner disclosed in the patent of S. W. Seeley, supra.

' This characteristic of the frequency sensitiveloop is utilized in Fig. l wherein the polarity is preselected, soas to effect the synchronization around the, upper 'sideband It is well understood in the artk that synchronization could be effected at the lower sidebai'ld by -transposing the output leads of the'rrequency discriminator H in Fig. fi.

A further point of difference between frequency and phase sensitive automatic control loops lies in the degree of frequency correction obtainable. A control loop employing a phase discriminator and associated reactano. tube alone is, as hereinllefore'v indicated, capablel of controlling the controllable oscillator, with zero frequency error."

Thislattribute is' disclosed in the patent of A.lF'. y

Pomeroy, supra. Frequency control circuits embodying only frequency discriminators are able to effect control to within a few cycles ofthe desired predetermined frequency difference, but are not capable of"zero frequency error, that is, of effecting 'control to the exact predetermined frey quency difference.

ofthe-phase discriminator I8-.

y and vto select the particular one desired.

Still another` difference isin the fresponse times of frequency'and phase ,Y sensitive automatic control circuits. Aslmay be seen *from Equation 3 above, lno corrective force ispresent in :aphase sensitive control loop at ythe instant of the application of a. ldisturbance which -disrupts the frequency synchronism between the inputs to the phase discriminator, since the Value of the integral in the latter equation is always zeno, at. 15:0.. Assuming that the disturbance were due tol an increment Afl, givento the frequency Fin Fig. l, the frequency of the controlled oscillator f Il! .does not immediately increaseby the increment Afr, given to F, but approaches the steady state along an exponential time curve. .A virtual delay is thus introduced into the phase |sensitive loop of Fig. 1 by the integrating action Y The ydelay occasione-dA vby integration issho-wn for the case yof the mechanical servo-mechanismv :in "Section (2.2.29, page v355, Theory of servo systems, with parti-cular reference to stabilizationby A. L.

wnitely, .published inthe I. E. Transactions,

may be written'.

Thel latter equation, stated in words, means that the controlled output shaft of the mechanism is regulate-d according to the integral of the shaft error between reference and output shafts, the factor Y v representing the' operation of integration in Heaviside notation. As E1 of Equation 3 herein is linearly rel-ated tothe output frequency of controlled oscillator I0, as shown in Fig. 3, it is apparent that the latter equation is the analogue to the Whit-ely Equation 8 and consequently the Whitely statement regar-ding the creation of -d'elay applies to the phase sensitive loop in Fig. l. As shown by Equation 4 above, no such virtual delay is introduced by the frequency discriminator I'I in the frequency sensi-tive control loop of Fig. 1.

. Also in Vconnection With the foregoing analysis, the controlled oscillator circuit of Fig. 1 may be viewed as one mesh frequency servo-mechanism `as illustrated in Fig.. 12 in which the quantity under control is the frequency of the vol-tage in the output of amplifier I6 in Fig. 1 and in which the vol-tage voutputs of the frequency and phase discriminators I-I Iand I8 in Fig. 1 are effectively applied in series to a single reactance tube whereby the oscillations of oscillator tube `3| in Fig. 2 may be .controlled in a manner that will now be explained. It is as equally valid to consider that the quantity specifically under control is the frequency of the voltage in the output yof amplifier I6, Vas it is to consider that the frequency of the 4controlled oscillator I 0 is under contro-l, since the former implies the latter. For this discussion, delays in such one mesh frequency servo-mech- -anism are neglected. In the circuit of Fig. 1 the control voltage outputs of the frequency and phase discriminators I'I Iand I8, respectively, are applied in tandem or in parallel to the oscillation tube 3| in Fig. 2. This is the same in an el-ectrical sense as when .the Voltage outputs of the two discriminators are applied in series to a single reactance tubev circuit for controlling the oscillation tube 3 I as just assumed for the purpose of further explanation and illustrated in Fig. l2. For this purpose the instantaneous velocities w1, wz, w3 and wi in Fig. l2 correspond to the frequencies previously identified herein regar-ding Fig. 1.

where E2 .and E1 are the voltages across condensers 52':and 62 in Figs. 4 and 6, respectively; a (wi-wz) is proportional to the frequency error between the voltage outputs of lamplifiers I6 and 22 .in Fig. 1;

is .the time integral of such frequency error; and the remaining terms represent values hereinbefore assigned.

Finally, in they foregoing analysis the controlled oscillator circuit of Fig. 1 may be viewed as a one-mesh phase servo-mechanism-as illustrated in Fig. 13 in whichv the quantity under control is the phase of the voltage in the output of amplifier I6 in Fig. 1 and in which the voltage outputs of the frequency and phase discriminators I1 and- I3 in Fig. 1 are effectively applied in series to a single reactance tube for controlling the oscillations of tube 3| in Fig. 2 in a manner that will be presently mentioned. For this discussion certain delays D1 and D2, representing, for example, those introduced by the integrating aspect of the phase sensitive loop, the tuned circuits of amplifier I I and multiplier I2, and the filter circuits of phase dscriminator I 8 and frequency discriminator I'I are considered. For this vpurpose the instantaneous angles 01, 02, 03 and 04 in Fig. 13 correspondV to the frequenciesl and the instantae neous velocities when, ai and wsrespectively, hereinbefore identified regarding Figs. 1 and y 12, respectively. v

From Equation 5,

Agb being the phase error of servo-mechanism. From Equation 4,

therefore,

Therefore,

' 01(01-02) a r`-, dt

Hence,

E1+E2=total voltage error (KAG) di is proportionaltothel derivative of such phase error. A Y

Thus, the derivative element (KAG) a di tends to stabilize the control of the over-all oscillator circuit lin Fig. 1 at the predetermined fixed difference Af relativeto the reference frequency F, ine., at the'upper'sideband F-I-nf, prevents lock-in at the unwanted sideband F-A'f, and in addition tends to preclude extraneous oscillation in the loop including the phase discriminator'l.

quency at which the. process of synchronization begins.. In. circuits 4employing onlyy phase vsensitive control, synchronization' is often difficult because of the rapidly changing phasesbetween the two voltage inputs'tothe phase discriminator prior to synchronization. Thev rate of Vchange of this phase is frequently greater lthan that which can be converted into a corrective voltage at the output of the phase discriminator because of' the time constant of the filter inthe output thereofas shown, for example, iny Fig. 6.V For this, reason the controlled oscillator l0 in Fig. l ist not fpushed into the desired synchronism with. the frequency F of the input voltage. As a consequence,a. state of extraneous oscillation oftenoccurs in phase sensitive control loops. This iscorroboratedin. an article The carrier-stabilization of frequency modulated transmitters, BrownBoyeri Review, August 19456, at page, 1,95;

Thep'rocess of. synchronization.y of the: synchronized oscillator l'of Fig.. 1 is rendered uncritical bytheV presence of the frequency4 discriminator I!!V therein. The voltage. at the outputof frequencydiscriminator I1, i. e., the charge on condenser.l 52 in` Fig. 4.,.is.` proportional, as'y hereinb'e.- fore mentioned, tol the rate of. change of relative. phaseV between the. tWo alternating'current inputs., i.. e., from amplifiers I6- and y22 in Fig; .1, to-the `phase discriminator' I8', andv therefore servesI tof slow down the rate of change of' such pljifase,` justl prior tolock-in at' thel desired predetermined frequency difference hereinbefore identified. The output` lter of phase discriminato'r 118.l in- Fig. 6'v can follow; this lessened' rate oflphase change; and asY a result the approach to the' desired frequency lockei'n proceeds smoothly.

. Moreover, the presence. of phase delays, ofthe type heretofore mentioned, in synchronized oscillator circuitsemploying only phase sensitive automatic control -le'a'ds to' instabil-ity of the's'ort encountered in mechanical servo-mechanisms whereinrelativelylarge inertiaelementsfare present.- f Such phase sensitive controlv loop is very often oscillatory dueto the response time lags.

In theY latter servo-mechanisman` effectivemeans of stabilization isv the addition'Y of-l derivatives of error to the-"error signalk applied at vthey input of the automaticVr controller for `sufch= mechanical servo-mechanisms. In theover-all synchronized oscillator of Fig.A l, the derivative control exercised Von the frequency of oscillation tube 3|/ residesrin4v reactance If!)V which is activated by derivativeof` error voltage from frequency discriminator H. The effectivenessof sol-calleddeivati've control instabilizing mechanical* servomechanisms' is disclosed in the 'Iheoryqof'servo Systems, with particular reference toV 'stabili-zationl by A. L. Whitel'yv in the I. E. El Transac-l tionsiyolume. 9-3; part II, 1946, at pages 353 and 358. v

It isj understood thatv the above control-princi'ple represented by Equation 6, is not' limited to its use in' the embodiment' disclosed above in Figs. 11,', 12' andV 13'... For Vexample, such principle lmay rbe'readily utilized by 'those skilled inthe art to maintainva controlled frequency equal' to that ofa reference source,A i. e., at a zero frequency .differencetherebetween This 'would mean that the controlled oscillator 'l0 in Fig. 1v couldv be'-v so 22 controlled by suchprinciple as t0 have a frequency equal to that of the reference frequency such. case, the frequency difference Af in Fig. lwould be zero.

Such principle may also be employed in the detection of frequency or phase modulated waves in. thefsense that itxmay be. used to effectively y narrow the frequency orv phase ldeviation thereof thereby permitting the use of a narrowerv band intermediate frequency amplifier in a receiver of such modulated waves. By Way of illustration, ifin. Fig. 12,. multipliers I2yand I5 were deleted, and phase or-frequency modulated` carrier frequencies: applied at-theNF input to mixer I3 the action ofv the automatic control loop would tend to. maintain a correspondence between the in'- stantaneous frequency or phase of oscillator l0 and frequency or phase deviations of the carrier NF, resulting in frequency or phase deviations in wz of lessened magnitude, thus permitting the use of a narrow band intermediate frequency amplifier whichv would conceivably be inserted between mixer l3 and the discriminators I7 and Theyoltages E1 and E2 Would then be` a measure of the instantaneous changes of modulation ofv the NF carrier applied to the mixer I3. A- prior art receiving system for frequencymodulated waves in which the above-described principlecould be used toV advantage is disclosed in the patent of J. Gr. Chaffee No. 2,118,161, issued May 24, 1938.

Another use. of such principle resides inthe generation. of frequency and phase modulated Waves wherein such modulation may be effected at a high degree of linearity. This may be seen from Fig. 12, where, due to the degenerative connections,` a highly linear phase deviation of the oscillator Il) would beA produced with respect to a modulating voltage inserted in series With the voltage E14-E2'.

vIn. addition tothe foregoing uses of the abovediscussed principle of. Fig. y1, it w-illbe understood that. further uses may be readilyvisualized by those skilled inA the art. p

What is claimed is:.. e

1. A system for rautomatically maintaining the frequency of the voltage of` a variable oscillator locked at a predetermined fixed difference from the frequency of a reference voltage source, comprising a frequency discriminator for producing a voltage in accordance with changes in the frequency of a component preselected from the combined oscillator and reference voltages, a voltage sourceY of standard frequency, a phase discriminator for producing a voltage in accordance with changes in the relative phase between said standard voltage and said preselected component, and means activated by said two discriminator'output voltages for varying the frequency y in which E1 and' E2 are the voltages applied. to

said activated means from said phase andfrequency discriminators,respectively; m and a, are the slope constants ofthe characteristics of'l the phasev and' frequency discriminators. respectively; (Aa)` is the Vchange of' relative phase betweenthe standard voltage and preselected com ponent'; mme) is `proportional. tosuchphase change ;1 and d(A0) dt` 23 is proportional to the derivative of such' phase change. V-

2. In a system for automatically maintaining the voltages of a variable oscillator and-:a referencesource electrically locked at a predetermined frequency difference therebetween, said oscillator including means for controlling the frequency thereof a mixer connected to said oscillator and source, a phase sensitive circuit," a frequency sensitive circuit, circuit means for applyingA a voltage of preselected frequency from the output of said mixer to the inputs of said phase and frequency sensitive circuits, said frequencysensitive circuit producing a potential varying in sign and magnitude in accordance with changesr in the preselected frequency ofthe voltage applied to the input thereof, a voltage source of constant frequency which is identical with that of said preselected voltage and which is applied to a second input of said phase sensitive circuit, said phase sensitive circuit-producing a voltage varying insign and magnitude in accordance with changes in the relative phase between the' constant and preselected voltages, and further circuit means for connectng the outputs'of said frequency and phase sensitive circuits to said oscillator frequency control means for translating changes of said potentials from said frequency and phase sensitive circuits into proportional changes f the frequency of said oscillator, said last-mentioned frequency changes automatically maintaining the frequency of said oscillator locked at the predetermined difference from the frequency of said reference source.

3. A system according to claim 2 in which the voltage applied from the output of said phase sensitive circuit to said further circuit means is proportional to the change in the relative phase between the constant and preselected voltages applied to the inputs of said phase sensitive circuit, and the voltage applied from the output of said frequency sensitive circuit to said further circuit means is proportional to the derivative of the change of relative phase between the constant and preselected voltages.

4. A system according to claim 2 in which the two voltages applied to said further circuit means have the form dma) di in which E1 and Ez are the voltages applied by said phase and frequency sensitive circuits, respectively, to said farther circuit means; m and a are the slope constants of the characteristics of said phase and frequency sensitive circuits, respectively; (A0) is the change in relative phase between the constant and preselected voltages; mmf?) is proportional to such phase change; and

(Ae) a di is proportional to the derivative of such phase change. Y

5. A system according to claim 2 in which said frequency sensitive Vcircuit is substantially instantaneously responsive to activate said further circuit means and therebysaid controlling means in response to a change in the preselected frequency of the voltage applied to the input thereof to vary substantially instantaneously the frequency of said oscillator, said last-mentioned variation in the frequency of said oscillator tending to reduce the change ofvsaid preselected frequency-and said phase sensitive circuit is thereafter responsive to the change of the relative phase between the constant and reference voltages to additionally activate said further circuit means and therebyv said controlling means to further vary the frequency of said oscillator,

said last-mentioned variation in the frequency of said oscillator tending to reduce to zero Ythe change of said preselected frequency.

6. A system according to claim 2 in which th frequency of said oscillator is automatically locked from the frequency of said reference source at a predetermined difference which has a numerical Value greater than zero.

'7. A system according to claim 2 in which the frequency of said oscillator is automatically locked at the frequency of said reference'source.

8. In an electronic oscillator having an output voltage whose frequency is controllable relative tothe frequency of a voltage supplied by a reference source, a generator of a voltage having a constant frequency, reactive means variable in eiTective reactance for controlling the frequency of said oscillator, means for deriving a voltage from one portion of a preselected output from the combined outputs of said oscillator and source, and means for deriving another voltage from the output of said constant generator and from a second portion of said preselected output derived from the combined outputs of said oscillator and source, said two derived voltages activating said reactive means to control the frequency of said oscillator relative to the frequency of said reference source, said second-mentioned derived voltage being proportional to the change of relative phase between said constant frequency and the frequency of the second portion of said preselected output derived from the combined outputs of oscillator and source, said first-mentioned derived voltage varying in accordance with the derivative of such change of relative phase. y

9. A system including an oscillator whosefrequency is controllable, a source of reference frequency, and means for automatically maintaining the frequency of said oscillator locked at a predetermined fixed frequency difference from the reference frequency, said means comprising a first multiplier for multiplying the reference frequency by a preselected factor, a second multiplier for multiplying the frequency of the controllable oscillator by said preselected factor, means forY `deriving from theoutputs of said two multipliers a voltage whose frequency is equal to the difference between the reference frequency multiplied bysaid preselected multiplication factor and the oscillator frequency multiplied by said preselected multiplication factor,va generator of a constant frequency which is eX- actly equal to the predetermined frequency difference between said oscillator and reference source multiplied by said preselected multiplicationV factor, a phase discriminator having two inputs one of which is connected to said generator and the other to said deriving means for producing an output Voltage proportional to the change in the relative phase between the constant frequency and the frequency of one portion of said derived voltage, a frequency discriminator having its input connected to said deriving means for producing an output voltage in accordance with a derivative of the change in relative phase between the constant frequency and the frequency of a second portion of said derived voltage, and reactivemeans connecting Ythe outputs 25 of said phase and frequency discriminators to said oscillator,v said reactive means translating said two discriminator output voltages into corresponding changes in the effective reactance of said reactive means whereby the frequency of said oscillator is automatically maintained locked at the predetermined xed difference from the reference frequency.

10. A system according to claim 9 in which further reactive means controls the frequency of said oscillator, and said connecting reactive means comprises two discrete reactive means, one of said discrete reactive means connects the output of said frequency discriminator to said further reactive means for translating the frequency discriminator output voltage into a corresponding change in the effective reactance of said further reactive means, and the other of said discrete reactive means connects the output of said phase discriminator to said further reactive means for translating the phase discriminator output voltage into a corresponding change in the effective reactance of said further reactive means, such two changes in the effective reactance of said further reactive means controls the frequency of said oscillator whereby the last-mentioned frequency is automatically maintained locked at the predetermined fixed difference from the reference frequency.

DANIEL LEED.

No references cited. 

